Related papers: Transfer matrix algorithm for computing the exact …
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
We present an algorithm for evaluating a linear ``intersection transform'' of a function defined on the lattice of subsets of an $n$-element set. In particular, the algorithm constructs an arithmetic circuit for evaluating the transform in…
We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
In this article we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when Gaussian basis set with pseudopotentials are used. The usual algorithm for evaluating exchange matrix scales cubically with the…
We consider the problem of finding a desired item out of $N$ items arranged on the sites of a two-dimensional lattice of size $\sqrt{N} \times \sqrt{N}$. The previous quantum walk based algorithms take $O(\sqrt{N}\log N)$ steps to solve…
The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…
The lattice $A_n^*$ is an important lattice because of its covering properties in low dimensions. Clarkson \cite{Clarkson1999:Anstar} described an algorithm to compute the nearest lattice point in $A_n^*$ that requires $O(n\log{n})$…
Runtime characteristics of sparse matrix computations and related processes may be often improved by reducing memory footprints of involved matrices. Such a reduction can be usually achieved when matrices are processed in a block-wise…
In practical applications, lattice quantizers leverage discrete lattice points to approximate arbitrary points in the lattice. An effective lattice quantizer significantly enhances both the accuracy and efficiency of these approximations.…
We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same…
We present a new class of particle methods with deformable shapes that converge in the uniform norm without requiring remappings, extended overlapping or vanishing moments for the particles. The crux of the method is to use polynomial…
The computational complexity of the self-attention mechanism in popular transformer architectures poses significant challenges for training and inference, and becomes the bottleneck for long inputs. Is it possible to significantly reduce…
We consider the problem of approximate counting of triangles and longer fixed length cycles in directed graphs. For triangles, T\v{e}tek [ICALP'22] gave an algorithm that returns a $(1 \pm \eps)$-approximation in…
We show how a Monte Carlo method for generating self-avoiding walks on lattice geometries which employs a binary-tree data structure can be adapted for hard-sphere polymers with continuous degrees of freedom. Data suggests that the time per…
We study self-avoiding walks on the square lattice restricted to a square box of side $L$ weighted by a length fugacity without restriction of their end points. This models a confined polymer in dilute solution. The model admits a phase…
While leverage score sampling provides powerful tools for approximating solutions to large least squares problems, the cost of computing exact scores and sampling often prohibits practical application. This paper addresses this challenge by…
A single-step high-order implicit time integration scheme for the solution of transient and wave propagation problems is presented. It is constructed from the Pad\'e expansions of the matrix exponential solution of a system of first-order…